The width of a rectangular fence is 5 feet less than the length. If the length is decreased by 3 feet and the width is increased by 1 feet , the area limited by the new fence will be the same as the area of the original fence. Find the dimensions of the original rectangular fence.

Length is 6 ft and

Width is 1 ft

Step-by-step explanation: The first clue we have been given is that the width of the rectangular fence is five feet less than it's length. So, if the length is L, the width is L - 5. From that bit of information on we can calculate the area if he rectangular fence as

Area = L x W

Area = L x (L - 5)

Area = L² - 5L

Also, the question further states that if the length is decreased by three feet (L = L - 3), and the width is increased by one foot (W = {L - 5} + 1 and that becomes L - 4), the area of the new enclosure would be the same as the first one. The area of the new enclosure would be given as

Area = L x W

Area = (L - 3) (L - 4)

Area = L² - 4L - 3L + 12

Area = L² - 7L + 12

Since the question states that the area of the original fence and the new one are the same, we can now write the following expression

L² - 5L = L² - 7L + 12

(That is, area of the first set of dimensions equals area of the second set of dimensions)

L² - 5L = L² - 7L + 12

By collecting like terms we now have

L² - L² - 5L + 7L = 12

(Note that when a positive value crosses the equation to the other side, it becomes negative and vice versa)

2L = 12

Divide both sides of the equation by 2

L = 6

Having calculated the length of the rectangular fence as 6 ft, the width is now derived as

W = L - 5

W = 6 - 5

W= 1

Therefore, the length is 6 ft and the width is 1 ft.

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.